Renormalized Area for Minimal Hypersurfaces of 5D Poincaré-Einstein Spaces

Abstract

In this paper we derive a Gauss-Bonnet formula for the renormalized area of Graham-Witten minimal hypersurfaces of 5-dimensional Poincaré-Einstein spaces. The formula we derive expresses the renormalized area in terms of integrals of pointwise scalar Riemannian invariants. We also prove a result which gives a characterization of minimal hypersurfaces with $L^2$ second fundamental form in terms of conformal geometry at infinity.

arXiv commentTypos have been fixed and the second main result has been re-phrased in order to emphasize the fact that it gives a characterization of minimal hypersurfaces with $L^2$ second fundamental form

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